Signal processing is directed to performing operations on or analysis of signals. Signals are analog or digital electrical representations of time-varying or spatial-varying physical quantities. Digital signal processing and analog signal processing are sub-fields of signal processing. Digital signal processing is for signals that have been digitized. Analog signal processing is for signals that have not been digitized. More particularly, digital signal processing represents signals by a sequence of numbers or symbols and the processing of these signals. Analog signal processing is any signal processing conducted on analog signals by analog means. “Analog” indicates something that is mathematically represented as a set of continuous values. This differs from “digital” which uses a series of discrete quantities to represent signal. Mixed signal processing includes elements of both analog signal processing and digital signal processing. Examples of mixed signal processing include, but are not limited to, comparators, timers, phase-locked loops, analog-to-digital converters, and digital-to-analog converters.
A fundamental distinction between different types of signals is between continuous-time signals and discrete-time signals. In the mathematical abstraction, the domain of a continuous-time signal is the set of real numbers or some interval thereof, whereas the domain of a discrete-time signal is the set of integers or some interval thereof. Discrete-time signals often arise via sampling of continuous-time signals. A continuous-time signal is a varying signal over a continuous time domain. A discrete-time signal has a countable time domain, like the natural numbers.
Signal processing systems can be either discrete or continuous in amplitude or time. Quantizers are used to convert signals from continuous to discrete amplitude, and samplers are used to convert signals from continuous to discrete time. Conventional digital signal processing systems are discrete in time and discrete in amplitude, but such systems suffer from aliasing and quantization noise. Conventional analog systems that process signals continuously in time and amplitude do not suffer from aliasing and quantization noise, but instead have high sensitivity to component tolerances and matchings, comparatively low dynamic ranges, and limited and difficult reconfigurability. Conventional systems that are discrete in time but continuous in amplitude, such as switched-capacitor circuits, also suffer from aliasing. Systems that are discrete in amplitude but continuous in time remain largely unexplored.
Signal processing has many applications. One such application is noise cancellation headphones which can be used to improve the quality of listening to an audio device in noisy environments. Many conventional high-end noise canceling headphones use analog components. When canceling an analog signal, a noise canceling analog signal is applied where the noise canceling analog signal is an inverse of the analog signal. The residue is the error (remaining signal) after the inverse signal is applied. The amount of residue is a function of the phase delay between the original analog signal to be canceled and the noise canceling analog signal. For effective noise cancellation to be achieved, real-time canceling is necessary. If the noise canceling analog signal is not applied within a relatively small phase delay, such as 10 degrees, much of the noise cancelling is lost. If the phase delay is less than this threshold, a good cancellation level is achieved. The higher the frequency of the signal to be cancelled, the more difficult it is to cancel the signal.
Current offerings use 100's of analog components at relatively high prices, approximately $300. A digital approach is feasible, but often with poor results or high costs because of the very low delay requirement for real-time noise cancellation. Digital filters used within noise cancellation circuits can provide more design flexibility than analog filters, but digital filters introduce delays and consume more power. Specifically, analog-to-digital conversion and digital-to-analog conversion needed in digital processing of analog signals require time and therefore introduce time delays. In applications that are real-time dependent, such as noise cancellation, such delays are prohibitive.